Intersecting rigid assemblies are required for the transmission of forces from one constituent member to the other, typical examples being a turbine in which a plurality of blades are mounted on a rotor; missiles or rockets in which guiding fins or rudders are mounted on a tail portion; and there are many others. In accordance with the prior art, the interlocking engagement of two constituent members of an intersecting rigid assembly is brought about by providing on the first constituent member an engagement portion with a plurality of transversal bores, providing on the second constituent member an integral pair of brackets with a plurality of pairs of registering holes, inserting the engagement portion of the first constituent member between a pair of brackets of the second constituent member so that each bore of the former is in alignment with a pair of registering holes of the latter, and tightening the two constituent members together by means of tightening members such as screws, bolts or rivets. In such prior art intersecting rigid assemblies, the tightening forces holding the two constituent members together are oriented predominantly in the direction of the tightening members. Accordingly, in order to provide the necessary resistance to the forces acting on the assembly, a relatively large number of tightening members is required which renders the assembling operation quite onerous.